Abstract
LetG, G′ be domains in ℝn. We obtain a geometrical description of the class of all homeomorphisms ϕ:G→ G′ that induce bounded operators ϕ* from the seminormed Sobolev spaceL p 1 (G′) toL p 1 (G) by the rule ϕ* u =u o ϕ. Forp-Poincare domains the same classes of homeomorphisms induce bounded operators for classical Sobolev spacesW p 1 . These classes of homeomorphisms are natural generalizations of the class of quasiconformal homeomorphisms that correspond to the casep=n. We demonstrate some applications of our results for embedding theorems in domains with Holder singularities.
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